Time Order F eq max Time Field mul
FieldSpecification.FieldOpFreeAlgebra.timeOrderF_eq_maxTimeField_mul
Plain-language statement
In the state algebra time, ordering obeys T(φ₀φ₁…φₙ) = s * φᵢ * T(φ₀φ₁…φᵢ₋₁φᵢ₊₁…φₙ) where φᵢ is the state which has maximum time and s is the exchange sign of φᵢ and φ₀φ₁…φᵢ₋₁.
Exact Lean statement
lemma timeOrderF_eq_maxTimeField_mul (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) :
𝓣ᶠ(ofFieldOpListF (φ :: φs)) =
𝓢(𝓕 |>ₛ maxTimeField φ φs, 𝓕 |>ₛ (φ :: φs).take (maxTimeFieldPos φ φs)) •
ofFieldOpF (maxTimeField φ φs) * 𝓣ᶠ(ofFieldOpListF (eraseMaxTimeField φ φs))Formal artifact
Lean source
lemma timeOrderF_eq_maxTimeField_mul (φ : 𝓕.FieldOp) (φs : List 𝓕.FieldOp) : 𝓣ᶠ(ofFieldOpListF (φ :: φs)) = 𝓢(𝓕 |>ₛ maxTimeField φ φs, 𝓕 |>ₛ (φ :: φs).take (maxTimeFieldPos φ φs)) • ofFieldOpF (maxTimeField φ φs) * 𝓣ᶠ(ofFieldOpListF (eraseMaxTimeField φ φs)) := by rw [timeOrderF_ofFieldOpListF, timeOrderList_eq_maxTimeField_timeOrderList] rw [ofFieldOpListF_cons, timeOrderF_ofFieldOpListF] simp only [Algebra.mul_smul_comm, Algebra.smul_mul_assoc, smul_smul] congr rw [timerOrderSign_of_eraseMaxTimeField, mul_assoc] simp- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/QFT/PerturbationTheory/FieldOpFreeAlgebra/TimeOrder.lean:318-327
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